Minecraft – install the own Minecraft skin in Xbox 360

According to the Minecraft Wiki, the Xbox version is closest to Beta 1.8.2. It is expected to be updated again.

Here are a few key differences between the versions. The full current list can be found here.

• Local 4 player split-screen multiplayer (requires HDTV, won't work on SD)
• Limited to 8 player online play (apparently cross platform multi, but not too sure about that)
• Newly designed crafting system
  • Seems to use a list for crafting, so you don't need to remember recipes
• World's limited to 862x862x128 blocks (PC is ∞X∞X256, expected to be increased in later versions)
• Cannot change difficulty mid-game
• Can't use mods, texture packs, or add player skins (8 skins included in game)
  • Texture packs and mods support is expected much later
• Includes tutorial mode
• Kinect support is expected to be added later

EDIT:

As of October 12th, 2012, the Xbox version was updated to include all features listed (here)

Minecraft for the Xbox 360 does have online voice chat enabled.

You can also create a party on Xbox live to voice chat with each other and then join the same hosted session in Minecraft.